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In Severedonetsk, in the neighbouring Luhansk region, none of the 50 polling stations were allowed to work.

Citing feedback from the 3,000-or-so election monitors in Ukraine, the NGO gave examples of how the anti-election operation is being carried out.

In Dokuchaevsk, in the Donetsk region, “a group of armed persons occupied polling stations” on Sunday morning.

In the village of Kalinino, Donetsk, a meeting of election officials was interrupted by men who “came into the commission's premises with weapons. The observer of the All-Ukrainian Committee of Voters was intimidated. The election commission decided to close the polling station.”

At a school in Severedonetsk gunmen “came into the premises for voting and broke two big ballot boxes … before leaving, the separatists told duty women not to open the door to anybody.”

A contact in Donetsk city, who asked not to be named, said pro-Russia groups also organised a rally of at least 800 people in the city's Lenin Square. He noted that another 100 or so gunmen came to the event: “It was pretty quiet. But at one point the armed men started shooting automatic weapons in the air [in celebration].”

The men later marched to the home of Ukraine’s richest man, Donetsk steel baron Rinat Akhmetov, in a show of force after he refused to back their call for the region to split from Ukraine and become part of Russia.

The presidential vote in Ukraine is seen as vital by the EU for stabilising the country.

But Western leaders fear that if voting is disrupted to a too great extent, Russian leader Vladimir Putin will declare the election was illegitimate, auguring an escalation of the conflict.

The Donetsk and Luhansk regions account for about 5 million of Ukraine’s 36 million voters and 20 percent of the country’s territory.

But people in Kiev and in the rest of Ukraine turned out in large numbers on Sunday: Another election monitoring body, Opora, said 25 percent of the country had voted by noon. In south-west Ukraine, 40 percent had voted by 1pm.

Despite the situation in the east, the atmosphere in Kiev on Sunday is quietly cheerful.

The Maidan, the plaza at the heart of February’s revolution, is hosting a karaoke concert.

With Kiev also electing a new mayor on Sunday, one group added to the fun by going to vote dressed as Storm Troopers - characters from the Star Wars films - for their mayoral candidate, a satirist who dresses up as Darth Vader.

Meanwhile, Arseniy Yatsenyuk, the caretaker PM, who is not running for president, was photographed waiting in a queue to cast his vote in a symbol of Ukraine’s new political culture: People in Kiev are more used to men in power cutting through traffic in fleets of black SUVs.

The leading presidential candidate, Petro Poroshenko, went to his voting station with his children. He called out "Glory to Ukraine!" - a revolutionary slogan - after casting his ballot.

He is expected to win by a landslide.

Krzysztof Lisek, a Polish centre-right MEP who is helping to monitor events in south-west Ukraine, told this website: “I heard from lots of people they plan to vote for Poroshenko so that he wins in the first round. They are telling me: ‘He’s no saint. But if we have to have a second round, it will be a mess, and it will give Russia a chance to exploit the situation.”

In a sign of the level of international interest in the election, an official at one polling station in Kiev told EUobserver that between 8am and 3pm, 343 people had cast their ballot and 62 journalists, from Europe, the US, Canada, and Japan had come to ask her questions.

For his part, Vasyl, 27, a Russian-speaking musician from Kiev, said he voted because Ukraine needs a new leader to bring it closer to the EU.

“Russia is corruption, the military, the police, lack of freedom. Europe is reform, opportunities,” he noted.

“It won’t be simple. [Russian leader Vladimir] Putin is very angry and doesn’t want to let us go. For him, Kiev is like his Jerusalem. But this is not the same country it was six months ago [before the revolution] and if we have a strong, legitimate President, we will win. Believe me.”

Alex, 30, a Ukrainian-speaking financial consultant from Kiev, said Ukraine needs a new President so he can conduct a military campaign to retake Donetsk and Luhansk.

He added that Ukraine should sign a free trade treaty with the EU even if it hurts the Ukrainian economy in the short term.

“Even if it brings economic disadvantages, it brings us closer to Europe. People who criticise the treaty do not understand the full implications of the process,” he noted.

“It’s about coming closer to the European vision, to a new way of life,” he said.

This story was updated at 6.30pm Kiev time to add the quotes from Vasyl and Alex

Opinion

While few people in Europe have heard of the 'Achmea' ruling, the case will have far-reaching consequences. Member states must understand the implications of the case quickly - especially those considering ratifying the EU-Canada trade agreement.